Statistical Models and Least Squares

Abstract

In § 3.5 we began a discussion of the concept of a statistical model; this is a very important concept, and most statistical analyses begin with a stage of setting up a model. We have a set of data before us, and we define a precise statistical model, which involves unknown parameters — the model to be such that it would generate data similar to the observations before us. All questions of statistical inference are then reduced to questions concerning the unknown parameters of the model. This leads on to problems of obtaining estimates of the unknown parameters from data, and problems of estimating confidence intervals, carrying out significance tests, etc. The purpose of this chapter is to illustrate further the model building stage of an analysis, and describe a general technique by which point and interval estimates and significance tests can be made for parameters in the models. In the first part of this chapter we are concerned simply with the idea of model building, and not with questions of how we use the model once it is formulated.